Vertical placement of line Conditioner: Any harm?

As long as the minimal needs for ventilation are not impeded, I doubt that you would run into any kind of a problem. In my system I run three equi/techs in just the same way. They remain switched on 24/7 and I never had any trouble.

I don't see why it would matter for a line conditioner. Now those line regenerators are a different animal, and I am not sure I would do anything unusual with them.

My Monster HTS-3500 has been vertical for 6 months, and seems to work the same as vertical placement. Just for fun, why not go to their website, and ask?

I ran a Transparent Audio Powerbank on its side for several weeks and had no problems.

Line regenerators (PS Audio, Accuphase) can be likened to amps, I suppose. I've run solid state amps on occasion vertically on the side, but not directly on the floor, but with something to stand them on, in order not to impede the flow of ventilation around the heatsinks. Never had any trouble. Would not want to try it with tubes. Have not done it with my PS Audio 300 and 600, but here I would not have any qualms about it, if I had to.